Question

How would the expression x^3-8 be rewritten using difference of cubes ​

Answer 1

Answer: The rewritten expression would be
`(x-2)(x^2+2x+4)`

Explanation:

Since we have given that

`x^3-8`

We need to use the difference of cubes:

As we know the formula of "Difference of cubes":

`a^3-b^3=(a-b)(a^2+b^2+ab)`

So, it can be written as

`(x)^3-(2)^3=(x-2)(x^2+2x+4)`

Hence, the rewritten expression would be
`(x-2)(x^2+2x+4)`

Answer 2

(x - 2)(x² + 2x + 4)

Explanation:

A difference of cubes factors in general as

• a³ - b³ = (a - b)(a² + ab + b² )

note 8 = 2³ = 8 ⇒ b = 2 , with a = x

Hence

x³ - 8

= x³ - 2³

= (x - 2)(x² + 2x + 2²) = (x - 2)(x² + 2x + 4)